Group #23744961 — subgroups

Subgroups — C₁₃×#10624810 #23744961

Order 9477.

238 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#6895	C₃	1	2	yes	maximal, complemented
2	C₁₃×#6887	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
4	C₁₃×#6868	C₃	1	2	yes	maximal, complemented
5	C₁₃×#6868	C₃	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#6867	C₃	1	2	yes	maximal, complemented
7	C₁₃×#6867	C₃	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#6866	C₃	1	2	yes	maximal
9	C₁₃×#6866	C₃	1	1	yes	maximal, characteristic
10	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
11	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
12	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
13	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
14	C₁₃×C₉⋊C₉	—	3	2	no	—
15	C₁₃×C₉⋊C₉	—	3	2	no	—
16	C₁₃×C₉⋊C₉	—	3	4	no	—
17	C₁₃×C₃²⋊C₉	—	3	1	no	—
18	C₁₃×C₃²⋊C₉	—	3	2	no	—
19	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
20	C₁₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
21	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
22	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
23	C₁₃×C₃²⋊C₉	C₃²	1	2	yes	—
24	C₉²×C₁₃	—	3	1	no	—
25	#10624810	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	C₃³×C₁₃	—	3	3	no	—
27	C₃³×C₁₃	—	3	1	no	—
28	C₃³×C₁₃	—	3	3	no	—
29	C₃³×C₁₃	—	9	2	no	—
30	C₃³×C₁₃	C₃³	1	1	yes	characteristic
31	C₃×C₉×C₁₃	—	3	3	no	—
32	C₃×C₉×C₁₃	—	3	2	no	—
33	C₃×C₉×C₁₃	—	3	1	no	—
34	C₃×C₉×C₁₃	—	3	1	no	—
35	C₃×C₉×C₁₃	—	3	1	no	—
36	C₃×C₉×C₁₃	—	3	2	no	—
37	C₃×C₉×C₁₃	—	3	2	no	—
38	C₃×C₉×C₁₃	—	3	2	no	—
39	C₃×C₉×C₁₃	—	3	3	no	—
40	C₃×C₉×C₁₃	—	3	3	no	—
41	C₃×C₉×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
42	C₃×C₉×C₁₃	H(3,𝔽₃)	1	2	yes	—
43	#6895	C₃×C₁₃	1	2	yes	complemented
44	#6887	C₃×C₁₃	1	1	yes	characteristic, complemented
45	C₃×C₃²⋊C₉	C₃×C₁₃	1	1	yes	characteristic
46	#6868	C₃×C₁₃	1	1	yes	characteristic, complemented
47	#6868	C₃×C₁₃	1	2	yes	complemented
48	#6867	C₃×C₁₃	1	1	yes	characteristic, complemented
49	#6867	C₃×C₁₃	1	2	yes	complemented
50	#6866	C₃×C₁₃	1	1	yes	characteristic
51	#6866	C₃×C₁₃	1	2	yes	—
52	C₃²×C₁₃	—	3	2	no	—
53	C₃²×C₁₃	—	3	1	no	—
54	C₃²×C₁₃	—	3	3	no	—
55	C₃²×C₁₃	—	9	9	no	—
56	C₃²×C₁₃	—	9	2	no	—
57	C₃²×C₁₃	—	9	1	no	—
58	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
59	C₃²×C₁₃	#737	1	3	yes	—
60	C₉×C₁₃	—	3	1	no	—
61	C₉×C₁₃	—	3	2	no	—
62	C₉×C₁₃	—	9	2	no	—
63	C₉×C₁₃	—	9	2	no	—
64	C₉×C₁₃	—	9	2	no	—
65	C₉×C₁₃	—	9	1	no	—
66	C₉×C₁₃	—	9	1	no	—
67	C₉×C₁₃	—	9	1	no	—
68	C₉×C₁₃	—	9	2	no	—
69	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
70	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
71	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
72	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
73	C₉⋊C₉	—	3	2	no	—
74	C₉⋊C₉	—	3	2	no	—
75	C₉⋊C₉	—	3	4	no	—
76	C₃²⋊C₉	—	3	1	no	—
77	C₃²⋊C₉	—	3	2	no	—
78	C₃²⋊C₉	C₃²×C₁₃	1	1	yes	characteristic
79	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
80	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
81	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
82	C₃²⋊C₉	C₃²×C₁₃	1	2	yes	—
83	C₉²	—	3	1	no	—
84	C₃×C₁₃	—	3	3	no	—
85	C₃×C₁₃	—	9	3	no	—
86	C₃×C₁₃	#6893	1	1	yes	characteristic
87	C₃×C₁₃	#6908	1	1	yes	characteristic
88	C₃×C₁₃	#6913	1	2	yes	—
89	C₃³	—	3	3	no	—
90	C₃³	—	3	1	no	—
91	C₃³	—	3	3	no	—
92	C₃³	—	9	2	no	—
93	C₃³	C₃³×C₁₃	1	1	yes	characteristic
94	C₃×C₉	—	3	3	no	—
95	C₃×C₉	—	3	1	no	—
96	C₃×C₉	—	3	2	no	—
97	C₃×C₉	—	3	1	no	—
98	C₃×C₉	—	3	1	no	—
99	C₃×C₉	—	3	2	no	—
100	C₃×C₉	—	3	2	no	—
101	C₃×C₉	—	3	2	no	—
102	C₃×C₉	—	3	3	no	—
103	C₃×C₉	—	3	3	no	—
104	C₃×C₉	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
105	C₃×C₉	C₁₃×H(3,𝔽₃)	1	2	yes	—
106	C₁₃	#10624810	1	1	yes	characteristic, direct product factor, Sylow
107	C₃²	—	3	1	no	—
108	C₃²	—	3	2	no	—
109	C₃²	—	3	3	no	—
110	C₃²	—	9	9	no	—
111	C₃²	—	9	1	no	—
112	C₃²	—	9	2	no	—
113	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
114	C₃²	C₁₃×#737	1	3	yes	—
115	C₉	—	3	1	no	—
116	C₉	—	3	2	no	—
117	C₉	—	9	1	no	—
118	C₉	—	9	1	no	—
119	C₉	—	9	1	no	—
120	C₉	—	9	2	no	—
121	C₉	—	9	2	no	—
122	C₉	—	9	2	no	—
123	C₉	—	9	2	no	—
124	C₃	—	3	3	no	—
125	C₃	—	9	3	no	—
126	C₃	C₁₃×#6893	1	1	yes	characteristic
127	C₃	C₁₃×#6908	1	1	yes	characteristic
128	C₃	C₁₃×#6913	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#6895

C₃

yes

maximal, complemented

C₁₃×#6887

C₃

yes

maximal, characteristic, complemented

C₃×C₁₃×C₃²⋊C₉

C₃

yes

maximal, characteristic

C₁₃×#6868

C₃

yes

maximal, complemented

C₁₃×#6868

C₃

yes

maximal, characteristic, complemented

C₁₃×#6867

C₃

yes

maximal, complemented

C₁₃×#6867

C₃

yes

maximal, characteristic, complemented

C₁₃×#6866

C₃

yes

maximal

C₁₃×#6866

C₃

yes

maximal, characteristic

C₃⁴×C₁₃

C₃²

yes

characteristic

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₃²×C₉×C₁₃

C₃²

yes

characteristic

C₁₃×C₉⋊C₉

—

C₁₃×C₉⋊C₉

—

C₁₃×C₉⋊C₉

—

C₁₃×C₃²⋊C₉

—

C₁₃×C₃²⋊C₉

—

C₁₃×C₃²⋊C₉

C₃²

yes

—

C₁₃×C₃²⋊C₉

C₃²

yes

characteristic

C₁₃×C₃²⋊C₉

C₃²

yes

—

C₁₃×C₃²⋊C₉

C₃²

yes

—

C₁₃×C₃²⋊C₉

C₃²

yes

—

C₉²×C₁₃

—

#10624810

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

—

C₃³×C₁₃

C₃³

yes

characteristic

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

—

C₃×C₉×C₁₃

H(3,𝔽₃)

yes

characteristic

C₃×C₉×C₁₃

H(3,𝔽₃)

yes

—

#6895

C₃×C₁₃

yes

complemented

#6887

C₃×C₁₃

yes

characteristic, complemented

C₃×C₃²⋊C₉

C₃×C₁₃

yes

characteristic

#6868

C₃×C₁₃

yes

characteristic, complemented

#6868

C₃×C₁₃

yes

complemented

#6867

C₃×C₁₃

yes

characteristic, complemented

#6867

C₃×C₁₃

yes

complemented

#6866

C₃×C₁₃

yes

characteristic

#6866

C₃×C₁₃

yes

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

—

C₃²×C₁₃

C₃×H(3,𝔽₃)

yes

characteristic

C₃²×C₁₃

#737

yes

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₉×C₁₃

—

C₃⁴

C₃²×C₁₃

yes

characteristic

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₃²×C₉

C₃²×C₁₃

yes

characteristic

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

C₃²×C₁₃

yes

characteristic

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₃²⋊C₉

C₃²×C₁₃

yes

—

C₉²

—

C₃×C₁₃

—

C₃×C₁₃

—

C₃×C₁₃

yes

C₃×C₁₃

yes

C₃×C₁₃

yes

—

C₃³

—

C₃³

—

C₃³

—

C₃³

—

C₃³

C₃³×C₁₃

yes

characteristic

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

100

C₃×C₉

—

101

C₃×C₉

—

102

C₃×C₉

—

103

C₃×C₉

—

104

C₃×C₉

C₁₃×H(3,𝔽₃)

yes

characteristic

105

C₃×C₉

C₁₃×H(3,𝔽₃)

yes

—

106

C₁₃

#10624810

yes

characteristic, direct product factor, Sylow

107

C₃²

—

108

C₃²

—

109

C₃²

—

110

C₃²

—

111

C₃²

—

112

C₃²

—

113

C₃²

C₃×C₁₃×H(3,𝔽₃)

yes

characteristic

114

C₃²

C₁₃×#737

yes

—

115

C₉

—

116

C₉

—

117

C₉

—

118

C₉

—

119

C₉

—

120

C₉

—

121

C₉

—

122

C₉

—

123

C₉

—

124

C₃

—

125

C₃

—

126

C₃

C₁₃×#6893

yes

characteristic

127

C₃

C₁₃×#6908

yes

characteristic

128

C₃

C₁₃×#6913

yes

—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₁₃
prime radical	C₃⁴×C₁₃	C₃²
LCS	G ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

subgroup

G/H

center, socle

C₃²×C₁₃

C₃×H(3,𝔽₃)

commutator, Frattini, cosocle

C₃³

C₃³×C₁₃

prime radical

C₃⁴×C₁₃

C₃²

LCS

G ▷ C₃³ ▷ C₃ ▷ C₁

UCS

C₁ ◁ C₃²×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

N	H ≅ G/N	type
1. C₁₃×#6895	C₃	semidirect
2. C₁₃×#6887	C₃	semidirect
4. C₁₃×#6868	C₃	semidirect
5. C₁₃×#6868	C₃	semidirect
6. C₁₃×#6867	C₃	semidirect
7. C₁₃×#6867	C₃	semidirect
25. #10624810	C₁₃	direct (N × H)
43. #6895	C₃×C₁₃	semidirect
44. #6887	C₃×C₁₃	semidirect
46. #6868	C₃×C₁₃	semidirect
47. #6868	C₃×C₁₃	semidirect
48. #6867	C₃×C₁₃	semidirect
49. #6867	C₃×C₁₃	semidirect
106. C₁₃	#10624810	direct (N × H)

H ≅ G/N

type

1. C₁₃×#6895

C₃

semidirect

2. C₁₃×#6887

C₃

semidirect

4. C₁₃×#6868

C₃

semidirect

5. C₁₃×#6868

C₃

semidirect

6. C₁₃×#6867

C₃

semidirect

7. C₁₃×#6867

C₃

semidirect

25. #10624810

C₁₃

direct (N × H)

43. #6895

C₃×C₁₃

semidirect

44. #6887

C₃×C₁₃

semidirect

46. #6868

C₃×C₁₃

semidirect

47. #6868

C₃×C₁₃

semidirect

48. #6867

C₃×C₁₃

semidirect

49. #6867

C₃×C₁₃

semidirect

106. C₁₃

#10624810

direct (N × H)

Subgroups — C₁₃×#10624810 #23744961

Conjugacy classes of subgroups

Complements

Subgroups — C13×#10624810 #23744961

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624810 #23744961